A. Use double integration to find the mass of thin plate with density: 6(x,y)= v5x' +10 of the region R bounded between the parabola: x=Jy and the line x=2 in the first quadrant ((0s ys 4).

Q: (2y – x*)dx + (4x + y²)dy where C is the boundary of the region in first quadrant bounded by x2 – 2x…

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Q: Evaluate the triple integral. 3x dV, where E = {(x, y, z) I 0 s y s 2, 0sxs V4- y², 0 s z s 2y}

A: Given region is E=x,y,z/0≤y≤2,0≤x≤4−y2,0≤z≤2y We have to evaluate the triple integral ∭E3xdV in…

Q: Write the integral as shown in the order dy dx dz.

A: The curve over which integration is being done is x = 0 and x = √1-y2-z2 Since we are changing the…

Q: d the volume V of the solid obtained by rotating the region bounded by the ren curves about the…

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Q: Sketch the region of integration, and find the best order of integrating, and then evaluate a· sec…

A: This is double integration so we will be  use in dydx form for solving integration.

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dx dy 3.

A: Answer and explanation is given below...

Q: Sketch the region of integration and change the order of integration. (x, y) dy dx f(x, y) dx dy

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Q: 2. Consider the region bounded by the graphs of y = 3* – 1 and x = y² – 3, illustrated at the right.…

A: The objective is to setup the integral that calculate the center of mass of the region bounded by…

Q: The given curve is rotated about the x-axis. Set up, but do not evaluate, an integral for the area…

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Q: Sketch in the xy-plane the region of integration for the integral /6 (cos 20 g(r, 0)r dr de. w/6…

A: Given Data The integral is ꭍ-π/6 π/6 ꭍ1/2 cos 2θ g(r,θ)rdrdθ.   The sketch of the region of…

Q: Find the average value of the square of the distance from the point P(x, y) in the disk x2 + y2…

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Q: Evaluate the double integral: 2 So de dy. Sola 0 Jy¹/3 Y x7 +1 (Hint: Change the order of…

A: Application of integration

Q: 1 dy dx 1+ y4 2. Sketch the region of integration, reverse the order of integration, and evaluate…

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Q: f(x, y) dx dy -2 Jo

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Q: Evaluate the integral. SSS_* √x² + z² av E where E is the region of integration bounded by the…

A: To solve this put x=rcos(theta) And z=rsin(theta)

Q: (6) Find the volume of the solid obtained by revolving the region between y = y = e¬¤ for 0 <x < ÷…

A:

Q: sketch the region of integration, reverse the order of integration, and evaluate the integral.

A: Given: ∫03∫x/31ey3dydx To Find: a. Sketch the region of integration.b. Reverse the order of…

Q: dy J 1+y+1

A:

Q: Sketch the region of integration, and find the best order of integrating, and e || 6x5 · e**y dA…

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Q: Q5A) Find volume of body from above Z=√√4-x² - y² and below Z = 1 using Triple integration.

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Q: Set up an integral for the volume of the solid generated by revolving the region in the first…

A: We can see the region bound by the curves. Now we will set up the integral.

Q: 4. Find the volume of the solid generated when the region bounded X - 2 by f(x) = x = 1, and the…

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Q: 2. Use a line integral to calculate the mass and average density of the helix ř(t) = (2 cos t, 2 sin…

A: The given data is: r→t=2cost, 2sint, t, 0≤t≤2πδx,y,z=z To find the mass.

Q: valuate the double integral. (x2 + 2y) dA, D is bounded by y = x, y = x³, x 2 0

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Q: Evaluate the double integral ff, cos(x²) dxdy exactly, where R:y<x< 1,0 <y< 2. Draw a picture of the…

A: We will find out the required solution.

Q: valuate the double integral. SL,(6x + 3y) dA, D is bounded by y = VT and y = r²

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Q: 3. Consider the region bounded by the y-axis, y = V3x + 1, and r = 4. Set up an integral to compute…

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Q: Solve for the area of the portion of the cylinder x = /1 – y², which lies between the planes z = 0…

A: Here is the solution of the given problem:  By using line integral to find the surface area of…

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dx dy 8 8- 2- 4. 8.…

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Q: 18. The integral that represents the volume of the solid obtained by rotating the region bounded by…

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Q: Sketch the region of integration, reverse the order of integration, and evaluate. cln z a dy dr

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Q: 4-x2 xe?y dy d.r, 4 - y Sketch the region of integration C, reverse the order of integration, and…

A: First I have see the limit of integration for x and y and then draw the region and then taking strip…

Q: Change the order of integration in the ihtegirul dx 1=, dy 1+Vi=y 1-VI-y (x-2x+y-3)² and hence…

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Q: Sketch the region R of integration and change the order of integration.

A: Given that,

Q: Evaluate the integral ∬Rxydydx, where the region of integration R lies in the sector 0≤θ≤π2 between…

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Q: You are rotating the region bounded by y 2 = x, y = 1, and x = 0 about the line x = 1. Set up the…

A: The graph formed After rotation it will look like Take the elementary element as

Q: Sketch the region R of integration and switch the order of integration. f(x, y) dy dx 2 1.5- -1 -0.5…

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Q: Evaluate the triple integral x dV where E is the solid bounded by the paraboloid x = 6y² + 6z² and x…

A: To evaluate the triple integral ∬∫ExdV where E is the solid bounded by the paraboloid…

Q: Q5A) Find volume of body from above Z = √√4 - x² - y2 and below Z = 1 using Triple integration.

A: I

Q: Hence, find the area of the specified region using integration. The base of a solid is the region…

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Q: D : y = V4 – x², y = V3x, x > 0 2

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Q: Find the area of R = {(x,y) € R² : x E[-1, 2], y e [x²,x + 2]} integrating first along horizontal…

A: Given region is   where curves are y=x2 and y=x+2

Q: x – 2 dx 9. J x² (x – 1)²

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Q: Realize Crane's theorem for linear integration (e* + y²)dx + (ey + x²)dy where c is the region…

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Q: Find the total differential of w ze(z+y) at (0,0, 1).

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Q: Change the order of integration of the iterated double integral: -8 r2 To for Y dx dy. 1/3 x7 +1…

A: Let's change the order of given integration.

Q: Sketch the region of integration, and find the best order of integrating, and 4ry dA with R bounded…

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Q: sketch the region of integration, and write an equivalent double integral with the order of…

A: Double integral:      ∫02∫04-y2 y dx dy=∫02∫04-y2 y dy dx

Q: 1–q² (b) Interpret Vr2 + y? dydx as a volume and calculate the integral without integrating.

A: b)

Q: Sketch the region of integration. '7 [In(x) f(x, у) dy dx y

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.